maybe she just feels akward with parents or has lots of work
her staying over would suggest that you are having sex?..or at least heavy petting..so what it basically translates as when she askes her parents is...can i stay over at my bf so we can do dirty things to eachother..i know that at school age i never felt comforable with having my bf stay over,telling my parens that i visited him, and i never stayed at his while parents are there..less so now because im over 18
also, girls are much more work conscious/worry more about grades (generally)..shes proabbaly keen to do well at school..im guessing since shes doing coursework that things/exams /work are hotting up, maybe she feels she doesnt have time to see you as much if she still wants to do well
i was VERY guilty of not spending as much time with my bf becuase of my A levels....
is she a hard worker, ambitious academically?..if so, thats probably why she doesnt want to stay over, maybe she hasnt finished her coursework